DIRECT MEASUREMENTS OF TOTAL REACTION CROSS SECTIONS BETWEEN HEAVY IONS FROM 10 TO 100 MeV/amu : PRELIMINARY CONCLUSIONS

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CROSS SECTIONS BETWEEN HEAVY IONS FROM

10 TO 100 MeV/amu : PRELIMINARY

CONCLUSIONS

J.F. Bruandet

To cite this version:

JOURNAL DE PHYSIQUE

C o l l o q u e C4, suppl6ment a u n o 8, Tome 47, aoiit 1986

DIRECT MEASUREMENTS OF TOTAL REACTION CROSS SECTIONS BETWEEN HEAVY IONS FROM 1 0 T O 1 0 0 MeV/amu : PRELIMINARY CONCLUSIONS

J.F. BRUANDET

I n s t i t u t des Sciences Nuc16aires. USTMG e t IN2P3, 53 Avenue des Martyrs, F-38026 Grenoble Cedex, France

R6sumb

-

Apres une revue des principales formulations thboriques du concept d e t i o n efficace t o t a l e de reaction OR dbveloppbes d'une part pour l e s collisions 5 basse energie (4 10 MeV/nucl6on) e t d'autre p a r t , pour l e s c o l l i - sions B haute 6nergie (-GeV/nucleon), deux mbthodes de mesure directe de q sont brievement presentdes (la methode d i t e de transmission e t l a mbthode du rayonnement associb). Les rbsultats experimentaux obtenus depuis 1982 dans l a gamne d'bnergie incidente de 10 B 100 MeV/nuclbon sont interpretbs dans l e cadre de deux approches theoriques diff6rentes : l'une bas6e sur I'intGraction potentielle Noyau-Noyau (mo&le macroscopique '%asse 6nergieW), l f a u t r e sur l e s interactions individuelles nucleon-nucleon (modsle microscopique %ahaute energie"). Divers p r o b l k s experimentaux e t thboriques r e l a t i f s B l'observable DR sont discutds e t quelques conclusions gbnbrales sont a l o r s avancbes. Le domine de l'energie de Fermi apparaTt

,

B trayers 1 'e'tude des sections e f f ica- ces totales de rbaction, cornme btant un bon domaine pour affiner nos concepts e t nos interpretations de l a vraie nature du noyau atomique.

Abstract

-

After a review of some theoretical formulations of the concept of t o t a l reaction cross OR, involving low energy (4 10 MeV/amu) and high energy

(> GeV/amu) models, two experimental methods used f o r d i r e c t measurements of

q , are presented, namely the "beam attenuation" and the "associated y-rays 4 a detection" nethods. Then a number of experimental r e s u l t s of OR i n the Fermi energy range i s given and the data are compared on the one hand with the predictions of the "low energy" BASS model (assuming a classical one- dimensional nucleus-nucleus potential interaction), and on the other hand with the predictions of a "high-energy" microscopic calculation performed using the formalism of KAROL (assuming that nuclear reactions are produced by individual nucleon-nucleon interactions). Finally, some experimental and theoretical problems are discussed and general conclusions are tentatively proposed.

I

-

INTRODUCTION

For many years heavy-ion t o t a l reaction cross

section so^

have been widely measured a t low energies (& 10 &#/am), OR being generally identified either with the fusion reaction cross section OF (see, f o r example, measurements of aF by direct observation of heavy recoil nuclei in bombarding different targets with a 32S beam / I / ) , or with the t o t a l cross section f o r production of f i s s i o n fragments OFF (see, for example, experiments in which2 3 B target was bombarded with various projectiles ~

/2/).

In contrast, i n the Fermi energy domain, there are u n t i l now only some pionee- ring data obtained i n the l a s t few years. The aim of t h i s paper i s to attempt t o a synthesis of almost recent r e s u l t s essentially concerned with direct measurements of OR in the 10-100 bV/amu incident energy range. The main sources of experimental

accurately a s possible,basic ideas and definitions relevant t o the interaction pro- bability of two colliding nuclei.

I1

-

THE BASIC FEATURES OF THE TOTAL REACTION CROSS SECTION 11-1 The classical geometric concept of OR

Two basic characteristics of nuclei have t o be taken into account t o define a measure of the nuclear reaction probability : one is the nucleus charge which induces a Coulomb trajectory e f f e c t , and the other is the spatial nucleon densit distribution the knowledge of which

is

fundamental to correctly express the r a t e

of

niclear reactions

Elementary concept of t o t a l reaction cross section OR is i l l u s t r a t e d on the figure1 which emphasizes the effect of the Coulomb repulsion in reducing the OR value, and r e c a l l s the central role played by the basic parameter R - t , referred t o a s the "(effective) interaction distance" which s e w o f e l a s t i c scattering and nuclear reaction in conkiguration space. For a given value of R i n t , we can write the well hown classical expression of OR :

which i s obtained from the conservation of angular momentum and energy along a clas- s i c a l trajectory. In t h i s relationship, V(Rkt) denotes the potential energy (Coulomb Vc + nuclear VN) a t the interaction distance, and Em the t o t a l kinetic energy i n

the center-of-mass system.

With Coulomb effect

,.--'

-.a % L

q = n

b,*.c

n

Ri"' b,,< R1.t

Fig. 1 Coulomb effect acts t o decrease OR

In order t o specify the importance of the Coulomb repulsion in the Fermi

n ~ h t an3 (Rint-bw) f o r the colliding systems 2 0 ~ e and Ca on 64zn and 2 0 8 ~ b , assuming :

-

an energy independent interaction dis- tance, namely with R, = 1.4 fm :

1 / 3 1/3)

Rint = Ro (Ap + At [

21

(that i s the crude approximation of the black disk model)

-

a nuclear potential contribution VN(Rint) =O so that

V(Rint) = Vc (Rint) = Zpzte2 / ~ i n t I t is clear that in most cases Coulomb e f f e c t must be correctly evaluated par-

ticulary f o r heavy systems.

The crude geometrical expression OR = nb& may be related t o a more refined formulation based on the usual summation of p a r t l a l (waves) cross sections :

Z

where Tg t s the transmission coefficient f o r the R-wave. In practice there w i l l be a transition region i n angular momentum space where the transmission coefficient varies smoothly form near-unity t o p r s i c a l l y zero. In a sharp cut-off model %step function i s used f o r the decrease of TR from 1 t o 0 a t a cut-off value R- (TR = 1 means t h a t a reaction occurs) and we can write :

For large values of !?.,ausing the semi-classical relationship R x - ' ~ , we find the ,

crude expression OR =

a

b&. 5jnceVel37 many p a r t i a l waves contribute t o a heavy-ion reaction it may be convenient t o replace the summation by an integral so that OR can also be expressed as:

4 d

the transmission coefficient TR being replaced by a transmission functicn T ($1 or

TT).

The sharp cut-off a p p r o x h t i o n thus yields t o the relations :

The limitin angular momentum

&

= (I./% is related t o Rint and

Em

through the relation

ak

which in f a c t i s directly derived from the energy conservation equation

Ec,q = ( h 2 / 2 u ~ h t ) !LZmax + V(Rint)

.

The p a r t i a l waves Formulation of a~ points out the

important contribution t o a of the various peripheral-type reactions, and emphasizes t h a t a good description of !he t o t a l reaction cross section needs a well-suited accom of the nuclear surface properties. A t t h i s point l e t us r e c a l l that i n its s t r i c t sense aR is defined as the sum of a l l non-elastic nuclear reaction channels.

Now we have t o give a more precise formulation of the interaction distance R h t . This distance must be expressed a s a function of the r a d i i of projectile and target nuclei, remembering t h a t the spatial distribution of proton and neutron in the nucleus has a strong influence on the r a t e of nuclear reaction. We then get in the maze ( I ) of the nuclear r a d i i definitions and analytical expressions /6,7,8/ (in addition t o the senmtic ambiguity "radius/distanceH t o describe the interaction of two nuclei). F u t h e m r e it i s now well established /9/ t h a t , a t least f o r the me- dium weight and heavy nuclei, the neutron distribution extend s l i g h t l y beyond the proton distribution. Presently neglicting t h i s f a c t (we should come back t o t h i s ques- Pion in the l a s t chapter) we give in figure 3 a schematic i l l u s t r a t i o n of the overla of the matter density distributions of projectile (p) and target ( t ) nuclei a t d

mteraction distance Rint

,

expressed a s being approximately 3 fm larger than the half-density distance R1/2 ( p t ) = Kl'/Z (p) + R1/2 ( t ) between the two nuclei

Rint z {Rl/z (p) + R1/2 ( t ) + 3 ) fm

161

A rough usual expression of the half matter density radius f o r a nucleus of atomic mass number A is :

R1lZ = ro = 1.1 fm C7'1

The fonmilationl61 of R a t provides a more useful representation of the interaction distance than the conventionnal parametrization [2] where the "radius parameter" R, varies systematically with target and projectile masses.

Fig. 3

-

(a) Experimental (solid line) matter density distribution and theoretical (dashed l i n e ) Fermi I distribution function. Radii definitions are those of reference/6/

(b) W t t e r density overla? of the two colliding n ~ c l e i ' + ~ ~ a + l l S I n a t the interaction distance R i n t = R1/2 ( Oca) + R ~ / ~ ( ~ ~ ~ I ~ ) + 3 fm

I t i s noticeable t h a t such a classical analysis of OR so f a r disregards nuclear

deformation : it is postulated that a l l the parameters involved in the UR expression have and keep a t the time of the collision a spherical symmetry (e. g. V(r)

,

P (r)

. .

.)

.

Obviously it is allowed to think t h a t dynamical nuclear deformations (dependent on impact parameter) may, in some cases, significantly perturb t h i s symmetry. However it i s assumed in f i r s t approximation that i n the Fermi energy range t h i s has a small repercussion on the

total

reaction cross section.

11-2-Nuclear transparency e f f e c t

For- many. years it i s experimentally established /I 0,11,12/ t h a t , for reactions

induced by light projectiles (such a s n,p,d?a) a t energies from several ten t o seve- r a l hundred MeV/amu there a r e strong deviations of the measured UR from the classical expression UR = a R h t [I

-

V/ECM

1.

The t o t a l reaction cross section does not "satu- rate" t o the geometric values aR&t a s increasing the bombarding energy : instead, a f -

t e r peaking a t a few tens of MeV/amu, the values of OR decrease steadily u n t i l a f t e r 100 MeV/amu is reached. Such observations have also been reported f o r r e l a t i v i s t i c heavy ions collisions /13/. This fall-off of OR a s a function of the energy i s refer- red t o a s a nuclear transparency. This nuclear transparency effect may be included in previously proposed classicaf formulations of UR.

A f i r s t way is t o modify the standard expression aR = a

RLt

[ I

-

( v c + b ) / b ] by writting

where T is a global transparency parameter varying a s a function of the projectile en- ergy and ?ffaneffective interaction distance taking into account the nuclear po- t e n t i a l ef e c t a t low incident energy. This approach has originally been developped for nucleon induced reactions by BETHE /14/

in

the form :

and then refined by

RENBERG

e t a l . /11/ with the modified formula :

which is the reciprocal of the mean free path of the incident nucleon in nuclear mat- t e r . The formulations [83 and [9] consist in f a c t i n reducing the interaction distance when bcreasing energy. An interesting conclusion of RENBERG e t a l . /11/ is that the transparency i s seen to decrease with increasing target mass number,i.e. the reaction cross section comes closer and closer t o the geometrical cross section. For r e l a t i v i s - t i c heavy ion collisions

a

rough parametrisation has been very early proposed /15/ referred t o a s the overlap model : =

TI%(^'/'

+ A ~ ~ / ~ )

-

AR]2 where AR i s the overlap term (of the order of magnitude of nuc ear force range).

An other way of taking transparency effect into account is t o s t a r t with the e ression [S] and then t o express the transmission function

~3)

i n the form

3)

=

11

-

T(b)] where T(b) is the so-called transparency function, which represents the probabilitythat a t impact parameter b the projectile w i l l pass through the target without interacting, so t h a t :

m

O R = 271 J o b l ~

-

T @ ) I db 1103

Thetheoretical calculation of UR is thus reduced t o the problem of calculating T(b),

which can be achieved in microscopic way assuming that nucleus-nucleus interactions r e s u l t from single nucleon-nucleon colli'sions in the region of overlap between pro- j e c t i l e and target. Some of the basic features of such interpretation of oR(mean free path A of nucleon i n nuclear matter; nucleon-nucleon t o t a l cross sections; e f f e c t =he Pauli exclusion principle on the scattering by a nucleon bound in the nucleus) have early (1949) been mentioned by

FERNBACH

e t a1./70/ who have explained transparen- cy observed i n high energy neutron-nucleus collisions. Later, an analytical formulatior of a o~ microscopic calculation, according t o (10

I

,

has been proposed by KAROL/13/ f o r high energy (GeV/arm) heavy ions collisions : in t h i s geometrical model, trajecto- ry Coulomb and nuclear e f f e c t s are ignored (straight l i n e path of colliding nuclei) a s a r e considerations of Fermi motion of nucleons within nuclei and Pauli Blocking e f f e c t (effect of the exclusion principle on the nucleon-nucleon scattering cross section inside nuclei), but the calculation of T(b) includes r e a l i s t i c matter densit distribution p (Gaussian functions a r e used for the whole distribution d i

and f o r the t a i l of distribution for heavy nuclei). The way on which the calculation is performed may be very briefly summarized a s follow : the local mean free path of the projectile moving i n the z axis direction a t impact parameter b i s defined a s

*(b,z)

=[F

.

Gt

(b,z)]

-'

11 11

-

P ( b ? z ) 1s the target-projectile overlap matter density (folding of the target

+

an projectile p t densities)

-

-

u p =

[(%zt

+ NpNt) $+

(Z&

+ NpZt) CJ?]/$,.A~ is the spin-isospin average nucleon-nucleon t o t a l cross section

-

4'=

a?# o r = ap: are the experimental (free diffusion) nucleon-nucleon t o t a l cross sections /16/=rhen the probability T(b) that the projectile undergoes no inte- raction a t impact parameter b is given by :

The dependence of T(b) (see fig. 4)-and thus of OR

-

on projectile energy is determi- ned by the energy dependence of the $ N ( s e e f i g . 5)

T

In t h i s formulation it is assumed t h a t the outgoing f l u in the i n e l a s t i c channels occurs by means of nucleon-nucleon collisions : only one nucleon-nucleon collision

is enough t o have a nuclear reaction event contributing t o OR. With equivalent high

energy approximtions a s those of the KAROL model, but describing the scattering by a f i r s t order optical potential in the impulse approximation, ERNST /19/ has fairly well reproduced OR experimental data f o r proton-nucleus collisions i n the energy

Fig. 4

-

"C + transparency function T(b) (from Ref. /1 7/)

LI

. .

. 1 . . . . I . . . 1 . . . . I

I

50 100 ace I c e 0

E, ( N u 1

Fig. 5 Nucleon-nucleon t o t a l cross-sections a s a function of incident lab. energy

(from Ref/l8/)

I t must be mentioned t h a t , although the KAROL'S calculation i s essentially geometric, the deduced f i n a l formulation of UR i s equivalent/l7/ t o the optical l i m i t of the

GLAUBER

theory /20, 21/. In t h i s theoretical framework, high energy collisions bet-

ween heavy nucleihave been extensively studied by FRANC0 /22/, and calculations of nucleus-nucleus OR in the Fermi energy domain (taking into account Coulomb effects) have been performed by DEVRIES e t a1 /18, 23/.

But the optical limit of the GLAUBER theory ignores Pauliblocking a s well a s the Fermi motion of the nucleons : the formalism has thus been refined by DiGIACOW, DeVRIES and PENG /24/ by including the e f f e c t s of the Coulomb potential, real nuclear potential, Pauli blocking and Fermi motion, providing a good description of the data for nucleon-nucleus collisions i n a broad range of energy (15 MeV through 1 GeV). An effective nucleon-nucleon t o t a l cross section in nuclear matter (Fermi and Pauli ef- r e c t s ) lwt be used : the figure 6 i l l u s t r a t e s the variations of the effective proton-

E~ I M ~ V I proton ufP (bound ) a s a function of the 41k?~ , 8: ,

171

, 2 ~ , , 4?3 , 572 , relative momentum of the incident pro-

10 ton and the target nucleus (KF is the

cPP~~..l radius of the Fermi sphere describing

r!Pd

~ F ~ ( b o u n d ) the target nucleus in the moment spa-

(mb) ce)

.

Calculations of effective u p i n the case of nucleus-nucleus collisions have also been pertormed by DIGIAC3W e t a l . /25/ i n a geometrical model. More recently TREFZ e t a l . /26. 27/

have propos~d a very elaborated micros- c o ~ i c ~arameter-free calculation of the

t t # . l ~ . I . I c I c r . l

15 K . Z O I F ~ - ' I heavy-;on optical potential, b u i l t

0. I. 2 . 3 4 . 5. 6 . 7 from the basic effective nucleon-nucleon

K I C ~ " , interaction. This model (Cf. FAESSLER1 s

..\.

...

,

Fig. 6

-

Calculated effective proton-proton t a l k , t h i s conference) provides a good t o t a l cross section in nuclear matter description of heavy-ion OR data in the

(from Ref. /24/) Fermi energy range.

In summary, the various microscopic approaches above-mentioned are more or

l e s s based on high energy approximations and it follows t h a t nuclear transparency is linked t o the energy dependence of the underlying nucleon-nucleon interaction. The level of sophistication of calculations varies with the energy range and mass

win

they a r e supposed t o describe. A t low energy ( Q 10 MeV/amu) the crude use of uT

(free) is a p r i o r i n o t justified and it seems very reasonable t o allow (in addition t o Coulomb effect) f o r nuclear "mean-field" effects such a s real nuclear potential (tra- jectory effect.%reasing OR a t low energy), Fermi motion,and Pauli blocking (nucleo-

potential t o increase OR i s due /28/ t o the deflection into regions of higher target

density, t o the increase of the relative velocity a t which the nucleon-nucleon c o l l i - sion occurs, and t o the increase of the path length within the target.

potential

-

nucleon-nucleon

10 100

Elab(MeVIA1

I . . . . I I , , , , I 1

. ...

1 , , ,

Fig. 7

-

The three ways two pieces of nuclear matter mike acquaintance 1.5-

111 - EXPERIMENTS IN THE FEW1 ENERGY WMAIN AND THEORETICAL INTERPRETATION OF RESULTS

Fermi motion

Pauli blocking

4

CR

c:'!.effective

(

cN-

free

111-1-Motivations t o undertake a~ measurements in the Fermi energy domain

As emphasized in the previous chapter, following the rather refined theoreti- c a l work O ~ D ~ G I A C O ~ DeVRIES and PENG /12,18,20,21/, who have succeeded i n descri- bing aR for nucleon-nucleus collisions in the 10-1000 kV/amu range, the question i s asked t o know t o what extent OR values for heavy-ion collisions may be explained in terms of individual nucleon-nucleon interactions. Such a question i s particulary per- tinent in the Fermi energy domain (transition domain between low ang high energy for the physics of the nucleus in colliding situation). This question may be extended to the more general problem of mechanism reaction analysis : i s the interaction between

two complex nuclei simply the incoherent superposition of individual nucleon-nucleon interactions or are there cooperative e f f e c t s such a s nucleon-nucleus or nucleus- pucleus interactions t h a t a r e qualitatively different ? However, with regard t o a ~ , it i s important t o realize that the problem i s not t o describe the dynamical evolution of the collision (that w u l d be necessary t o perform the calculation of a p a r t i a l cross section relevant t o a specified reaction mechanism) but simply t o describe the

i n i t i a t i o n of any reaction. So, the question must be a d d r e E d in a more precise for- mulation : t o what extent, in the Fermi energy domain, the i n i t i a t i o n of a nuclear reaction may be governed by incoherent individual nucleon-nucleon collisions or by

"mean field" interactioq keeping in mind the fundamental role played by the nuclear surface (i.e by the t a i l s of nucleonic distributions)

.

Obviously, a pragmatic motiva- tion t o measure heavy-ion OR in the 10

-

100 MeV/amu range, is also the current in- creasing of experiments in t h i s realm.

'

nucleon-nucleon

.*:,...

:

.

-

V)

.::...

.

-..

..',...

...'.

..

.:.-

.*

.':

E

-=:

1.-

nucleus-nucleus

-

be

-

_-

,

coulomb

-

G L

111

-

2-Direct measurements of aR

Values of OR may be extracted from e l a s t i c scattering data but they are then t o some extent model dependent. I t is therefore considered wrthwile t o obtain direct measurements. Two complementary methods of direct measurement (having in common the fact that -they involve mu1 t i-counters detection) have been recently used /3,4,5/ :

I I I-2- 1 -Measure~g;s-ug$g the gttenuat_igg-megngG

This method /29/, the up-to-date version /3/ of which i s shown schematically in Fig. 8, consists i n measuring, f o r a given number

NB

of incident beam particles, the number NT of beam and

:

;

:

!-~q:::@

e l a s t i c a l l y scattered p a r t i c l e s a f t e r passage through the target. The dif- ference between t h i s two numbers i s 1finn€r - - . directly proportionnal t o OR :

arm 4

u~

= K (NB

-

NT)/NB where K accounts

- - - _{for the target thickness. The counting}

s _{- - - . - -}

cam of NB (- 5.104 particles/s) i s provi- DWI ded by the thin s c i n t i l l a t o r counter

"1" anticoinciding with the active collimator "2" (referred t o a s

B = 1

.T).

The p a r t i c l e s a f t e r the tar- Fig. 8

-

Schematic of the experimental Setup get must be not only counted but a l - used in the attenuation method so characterized in order t o discri-

(from Ref. /3/) minate the non-reacting particles against the reaction products. This is achived by the means of a "wheel" arrangement (cylindrical syrmnetry around the beam axis) of 19 thin AE p l a s t i c s c i n t i l - l a t o r s , each of them furnishing a g i g h t signal (charge and energy dependent) and allowing a Lire-of-flight measurement with respect t o the counter "1". An ident i f ica- tion is made by using the two-dimensionnal plot AL

-

t : the charge identification of l i g h t heavy-ion projectile (Z

4

10) i s quite good but the separation of inelastic scattering and neutron-transfer reaction from e l a s t i c scattering i s not always unam-

biguous and corrections have t o be included i n the extraction of OR values. The cen- t r a l detector "3" sees the direct beam, the major part of e l a s t i c events, and some reaction products : in f i r s t approximation t h i s detector gives the number NT previous- l y defined

[

N ("3")

e

NT]

,

and t h s difference NB

-

NT may be electronically b u i l t by means of the anticoincidence [B.3

1

.

Target-in/target-out measurements are necessary t o correct f o r reactions induced i n counLers "1" and "3", ~p that a f i r s t raw deter- mination of aR is given by OR = K . .

[

B. 3 (target in)

-

B.3 (target out)

] .

Then, various corrections must be included in the f i n a l determination of OR. Target reac- tion products detected in counter "3" mst be substracted, and e l a s t i c events detec- ted i n the counters mosaicsurroundingthe central "3" s c i n t i l l a t o r must be added

(after evaluation of inelastic scattering and neutron-transfer). Other corrections due t o the geometry of the apparatus mst also be taken into account : the e l a s t i c scattering outside the cone covered by the detector arrangement and the loss of elas- t i c events in the inefficient detection regions corresponding t o the mechanical sup- port of the s c i n t i l l a t o r s (these corrections a r e the most important ones when

Z (target) '

>

30). A more detailed discussion of the experimental setup performances

may be found in the KOX' s t h e s i s /30/. The attenuation method is particularly well- suited t o measure OR of l i g h t heavy-ion collisions : the algebraic sum of the various corrections t o raw measurements remin generally l e s s than 15% of O R and the associa-

ted uncertainties contribute about 40% of the f i n a l error on CSR.

z

y

i

n

t

;

using t h i s apparatus have been performed with the beam (83 MeV amu o t e synchrocyclotron a t CERN, and with and 2 0 ~ e beams delivered by the SARA f a c i l i t y (30 MeV/amu) or the SATUNE f a c i l i t y (between 100 and 300 MeV/ am1 /3,5,31/. Such a systematic study of OR a s a function of the energy clearly

L

10 I b o ' " d o 0

tl,blMeVHI

EIabIMeVIAl

Eig. 9

-

Variations of OR a s a function of the projectile energy. The f u l l curves represent microscopic calculations (From Ref. /5/)

Direct measurements of OR can be achieved in principle by integrating over the yields of a l l possible reaction products : in the radiative detection method using a 4

s

NaI detector, heavy-ion collisions events a r e characterized by the observation of the induced y-ray transitions (moreover some additional l i g h t particles a s .neutrons or energeticprotons can be detected). The basic assumption of t h i s method /4,32/. is

that each nuclear reaction (obviously scattering process excluded) is necessarily fol- lowed by the emission of a t l e a s t one y-ray (or one detectable energetic l i g h t parti- c l e ) . The GANIL y-ray modular sum spectrometer has been used a s 4 .rr detector in the experimental setup schematically described i n Fig. 10. The detector assembly i s b u i l t - up from 14 separate large volume NaI counters surrounding the target i n an a rcxima- t e l y 4 n geometry. (Total solid angle nl4n = 0.93). The efficiencies E f o r 1 3 % ~ y-ray

(0,66 MeV) and 6 0 ~ 0 y -rays (1 , I 7 MeV and 1,33 MeV) are respectively 0.8 and 0.9. The detection probability of a reaction involving My-ra s can be expressed a s P M = ~ - [ I - w h i c h f o r ~ = 0 . 8

(i.e assuming

f'g

0.7 MeV) leads t o

P2 = 0.96 andP3 = 0.99.

There are three kinds of y-rays :

the good one "G1', the bad one "B" and the forged one "F". The "G" a r e the prompt y-rays issued-he target :

they are time-correlated with beam bursts and detected in coincidence with

the accelerator R F signal, The *'BB" have several origins : [al r e s i d m i o a c - t i v i t y in tKe target- (small contribu- Fig. 10

-

4 ITY experimental setup tion &en rather thin targets are used,

i.e. .J1 mg/cm2)

-

(b) various room back-

grounds,

;'

drastic attenuation of which was performed by low activity lead shielding of the NaI counters

-

(c) proper a c t i - vity of NaI material induced by l i g h t particles reactions..

.

it i s recommanded not t o send the beam outside the target ! -(dl y-rays from secondary reactions induced by e l a s t i c a l l scattered projectiles interacting with the chamber material.

In

order t o these y-rays from the

target-reaction's y-rays,

the design of the reac- t i o n chamber includes a conic e x i t extension (opening half-angle 0 E lo0, length r 2 m)

chamber. It is essential to note t h a t t h i s method is based on a single type detection of unidentified y-rays (except the time discrimination using the RF signal). I t thus

inrplies the use of a low intensity [<. 10' p/s) but high-quality beam (small emittance, good s t a b i l i t y ) and the need f o r a permanent checkup of the beam alignmnt (equaliza- tion of-counting r a t e s of four S i (Li) detectors, synnnetrically mounted around the beam axis). Obviously target-in/target-out measuremnts were also performed in order t o verify that the size of the beam and the level of the background radioactivity we- r e quite acceptable. Three types of beam monitoring were used : the Faraday cup beam charge integration, the Rutherford scattering measurements and a relative mnitoring based on the detection of K X-rays from atomic collisions induced by the beam on a gold f o i l (positioned nearby the entrance of the Faraday cup). The consistency of these three monitorings was required t o valid a measurement of OR.

The availability of a 4 .rr multidetector counter greatly renewes the radiative mthods of cross section masurements /33/ : detection efficiency is a small source of error, dead time corrections my be avoided, and selection conditions on the

multiplicity ("folds") my be used.

The principal contributions t o the f i n a l error on G R (=- 10%) are the uncertain- t i e s on target thickness and beam dose determinations. Moreover it must be mentioned that the experimental OR values resulting from radiative measurements include the

contribution of Coulomb excitation which has t o be considered a s a systematic error. This contribution however do not exceed sew percent of 0Ra-t incident projectile energy of several tens of k V / m (a calculation performed with the code ECIS,for the

44 MeV/amu O A ~ + O 8 Pb system,gives ~(Coulex) 2 1% of OR /34/) and thus i s within the data associated uncertainties. Such a problem has been discussed by OESCHLER e t a l . /35/ about the determination of OR from e l a s t i c scattering data when Coulomb

excitation is important.

Experiments using the above described

setup have been perfornted with a 'ONe beam s

-

(30 MeV/amu) from the SARA f a c i l i t y and

with the O A r (44 MeV/amu) and 4 0 ~ a ( 7 7 MeV/amu) 4

-

beams provides by the GANlL accelerator.

The aim was t o get a f i r s t quite large sampling of GR values, in the Fermi ener-

gy domain, for medium-light projectiles and a wide range of target masses. Such

direct measurements (which are a matter 30 ~ e ~ ~ a m v for the radiative method) a r e not inten-

ded t o provide an experimental i l l u s t r a - tion of nuclear transparency but rather t o furnish a preliminary database in or- der t o t e s t various theoretical predic- tions. Some resulting values of OR are displayed in Fig. 11, with t h e i r cor-

resp nding errors bars, a s a function

₉

Fig. 11

-

Plots of UR values a s a of Rlnt a s defined by formula [6]

.

function of R&

I t w i l l be noted t h a t OR r e s u l t s obtained from the radiative method for Ne

induced reactions are in excellent agreemnt with the data obtained from the beam attenuation method f o r l i g h t and medium-light targets.

111-3-Data analysis and discussion

tion, it may be interesting t o f i r s t consider the "degree of (disagreement", with experimental data, of the straight formulations of l~nucleus-nucleus" and "nucleon- nucleon" models. Next, the usefulness of a refined mixture of t h i s two approaches can be discussed (any nuclear reaction s t a r t s with a nucleon-nucleon collision).

as-

-'..

The energy dependence of aR data for l i g h t col-

liding systems (see ig. 9) bears striking ressemblan-

ce t o that of the a$ data shorn in fig. 5. This ob- a.

_{+ ,}

,

I /

servation strongly suggests an interpretation of the

nucleus-nucleus t o t a l reaction cross section in terms -. CALCUL. 0.0 of individual nucleon-nucleon collisions. The KAROL

formulation was used /5,31/, slightly m d i f i e d in or-

-

der t o take into account the trajectory Coulomb effect j

,

which i s not inconsiderable a t medium energy : in for-

b

mula [lo] T(bS) is substituted f o r T(b) with b' being the classical distance of closet approach correspon-

,,.

ding t o the (asymptotic) impact parameter b. Agreement with e erimental data is quite good for l i g h t systems "C + C' or "Al, and reasonably meaningful for the I -

medium-light systems (see f i g . 9 and 12). I t must be

mentioned that calculations of PENG e t a1 /23/ f o r fo io 3b lo 5b

+

12c

reaction also give a successful description Fig. 12

-

Fxperimental-oR data of the UR(E) data. Moreover

a

new semi-empirical pa- and KAROL'S calculations r a m t r i z a t i o n formula of oR has been proposed by Kox (from Ref ./30/)

e t a1 /31/, which gives good predictions (within a

precision of about 10%) in the Fermi energy range f o r

"c,

ON^

and ' O A r induced reac- tions. This formula i s in f a c t an elaborated expression of the overlap model / I S / , in- cluding mass asymmetry and energy dependent transparency terms.

The large sampling of % valms obtained with the radiative method has been compa- red with predictions of BASS model and of KAROL model. The BASS formulation /7/ is expressed through the classical relation- ship [ I

7

using : (i) an energy independent interaction distance, s t r i c t l y defined in configuration space a s

Rint = R1/2 (p) + R 1 i 2 ( t ) + 3.2 fin with R1/2 (A) = 1.12

-

0.94 A - ' / ~

( i i ) a potential energy

V(Rint1 = zpzte2

-

!1/2(p)

.

R l / ~ ( t l Rint _{R1/2(~) + R I / ~ ( t l}

best agreement : t h i s observation m y be Fig. 13

-

Experimental QR data and _{related t o the f a c t t h a t the influence on} theoretical calculations in the BASS

and XAROL models OR _is values of the transparency phenomenon _{greater f o r the l i g h t systems than for} the a t t r a c t i v e nuclear potkntial 'kontribu- tion being derived from the liquid drop model (b E 1 Me~.~m-l). I t must be empha-

sized t h a t the nuclear contribution takes into account surface e f f e c t s including an a s m e t r y term R(p)

.

R C ~ ) . / [ ~ ( p ) + ~ ( t ) ] t o be related t o the volume overlap of the colliding nuclei. The experimental OR va- lues and results of calculation i n the

the-heavy ones /30,31?. . ,-- M~croscop~c calcutat~on

f . , .

BASS an KAROL models a r e displayed i n - 1 Fig, 13. For the heaviest colliding systems 102 150 R& (fm2)

im

the BASS formulation provides a reasonable

n e s e general conclusions point out som need f o r an mrovement of straight mi-

croscopic calculations by taking into account mean f i e l d effects, that has been per- formed by DiGIACOEilO e t a1 /23,24,25/ and by TREFZ e t a1 /27/. I t w i l l be noted that experimental OR data f o r the reactions induced by 44 MeV/amu " ~ r projectile /4,37/ are i n good agreement with the theoretical predictions given in Ref. 27. Furthermore microscopic calculations must intend t o reproduce not only OR data, but also diffe- r e n t i a l e l a s t i c and inelastic diffusion cross section data /37,38,39/, remenbering that some cancellation effects /24,28/ can make the comparison with experimental data somewhat tricky. With regard t o heavy colliding systems it i s noticeable that Coulomb e f f e c t leads t o reduce, on the one hand the energy range in which the decrease of OR may be observed, and on other hand the importance of t h i s decrease (see Fig. 14 from Ref. /IS/.

The dominance of nucleon-nucleon interactions a t

,",

' I ' I I.', ' I ' I . 1 " _{medium energy is suggested on the basis of the agree-}

ment between microscopic calculations and experimen- t a l OR data (particularly f o r l i g h t colliding sys- terns). A more direct suggestion of t h i s behavior is furnished by the observation of the decrease of col- lective s t a t e s excitation (which take place via mean-field interactions), when increasing incident energy. An i l l u s t r a t i o n of such observation i s given

in figure 15 (form Ref. 39) which clearly exhibits the absolute and relative decrease of the excitation of the 2' (4.4 MeV) s t a t e of I 2 C , observed

in

1 2 c +

12c

inelastic scattering.

As a l a s t r e m r k , i t must be emphasized t h a t in microscopic approach of OR calculation, the 240a- exact spatial distribution of nucleons i s a funda-

,..I . 1 I . , . . , . I

.

I . L ,

I D Y) w m m m%wm

L. /p#MUl mental ingredient. A t some level of sophistication

of calculation, it would become relevant t o take into account the f a c t that protons and neutrons Fig. Microscopic predict ions densities distributions a r e different /6,40/. Then from Ref.

/

18/ _{the question of a neutron skin effect on OR value}

must be addressed /19,30/ f o r heavy-ion collisions.

-

_{Measurements of OR p e r f o m d either with beam}

on 6 4 , 6 6 y 6 8 Z n targets /31/, or with

ON^

beam on

1 4 4 , 1 5 0 y 1 5 4 ~ t, _{rgets /36/, do not allow t o actual-}

\.

l y conclude in a quantitative way considering the

20. errors bars (see Fig. 16)

I . n 002. ""' 10 50 100 E , ~ ~ / A (MeV) Fig. I S - E x c i t a t i o n f w r t i o n Is- , -3

of the collective 2+ s t a t e of (A?+A;~)' ,' 2 0 4 0 6 0

1% (from Ref. /39/) : + do & sb

(a) absolute variation 02

(

43+/2<3

)'

(b) relative variation 02+/oR

Fig. 16

-

Isotopic targets oR measurements (a) with projectile

(b) with 2%e projectile

IV

-

SUNWRY AND CONCLUDING REMARKS

In t h e i r r i n c i l e s , experimental measurements and theoretical calculations of UR are r a t h e r s w F i n r t i c e , t o . o b t a i n very accurate data and perform very f i n e ca c atlons we mst a t t t it is not so ea-sy. We m s t also be well-advised t o derive general conclusions from the present r e s u l t s of heavy-ion u~measurements in the Fermi energy range, keeping in mind that UR is a global quantity, the variation of which can only give global -but nevertheless fundamental- informations with regard t o nuclear collisions, essentially a t large impact parameters.

The widely systematic study of OR, a s a function of the projectile energy, f o r some l i g h t colliding systems /3,5;39/ (e-g. 1 2 C + 12C) strongly suggests t o link the energy dependance of UR with the behavior of the t o t a l free nucleon-nucleon cross sec- tions : t h i s could a t t e s t t o the dominant role of individual nucleon-nucleon c o l l i -

-

_{sions i n the Fermi energy domain /41/. For heavier colliding systems, measurements}

have been performed /4,36/ using various projectiles ( 2 'Ne,

'

'Ar

,

'

O C ~ ) of different

energy, in the framework of a systematic study of UR f o r a wide range of target masses; a reasonable overall agreement i s found with the predictions of the standard theory based on the one-dimensional nucleus-nucleus interaction uotential. but t h i s does not exclude agreemnt with microscopic calculations based on ;'effectiv&" nucleon-nucleon

interaction (thus including mean-field effects a s Fermi motion and Pauli blocking /27/),

D n t i l

we get more numerous and more precise experimental data it would be probably

_

hazardous t o extrapolate a l l the conclusions of

12c

+ 1 2 C measurements t o a Xe + Pb reaction (e.g.). Nowadays we can only conclude that the respective roles of "mean- field" and "nucleon-nucleon" aspects in a microscopic description of UR have t o be discussed and c l a r i f i e d taking into account the mass and energy domains of the c o l l i - sion.

The pieces of nuclear m t t e r that w c a l l nuclei ( f i n i t e many-body systems) have a specific property which is the existence of a natural boundary, namely a dif- fuse surface the role of which is fundamental in theoretical interpretation of u r Nuclear transparency (in the Fermi energy range) i s a phenomenon which occurs essen- t i a l l y in the nuclei overlap regions associated t o low matter density : it is thus concerned with the t a i l s of nucleonic distribution, which have approximately the same extent f o r any nucleus (A >, 121, the value of the surface t h i c h e s s parameter

( t 10

-

90%) being more or l e s s equal t o 2.2 fm. As a consequence of t h i s surface pro- perty, the (energy dependent) "transparent" region has, a t a given projectile energy, very roughly the same extent on impact parameter scale whatever the colliding system i s considered. I t follows t h a t the r e l a t i v e influence of transparency phenomenon on

UR value i s greater f o r a l i g h t s y s t e m . C + C) than f o r a heavy one (e.g. Ar+Pb)

.

For heavy systems the study of ( i n ) e l a s t i c diffusion cross-sections may be a comple- mentary or a more convenient way t o investigate the energy dependence of the trans- mission function /37,39/. I t must be also mentioned t h a t the reasonable success of the optical l i m i t of the Glauber theory in describing UR is probably due t o the cen- t r a l role played by the low matter density surface of the nuclei /42/.

Describing the nuclear collision cross sections in a microscopic way i s ob- viously a very ambitious task, but it i s an usual challenge f o r nuclear physicists

(who have sometimes succeded i n microscopic interpretation of spectroscopic proper- t i e s of n x l e i ) . The basic feature of such calculations i s the evaluation of the ef- fective nucleon-nucleon interaction i n nuclear matter under nucleus-nucleus colliding situation. Almost recent theoretical works /25,27/ are, a t l e a s t , encouraging. But it

is very evident t h a t an experimental data improvement i s needed t o accompany theore- t i c a l developments : more measurements with a good accuracy (< _{5%) should be underta-} ken i n a "metrological" ("spectroscopy liket')way, t h a r does not necessarily m i y a very large systematic work. For instance, it would be interesting t o perform UR mea- surements f o r some isotopic series in order t o investigate the neutron skin effect. From a more pragmatic point of view, additional UR data would be also of interest

t o check up on the validity domain (mass and energy) of various parametrization for- mula of OR /7,31,43/.

ACKNOWLEDGEMEWS

I t is a p l e a s u r e t o acknowledge my colleagues G . J . COSTA, Y. EL-MASRI, S. KOX, E. LIATARD and TSAN UNG CHAN f o r m y s t i n u l a t m g t a l k s . I am a l s o indebted t o

M. BUENERD, J. CHAUVIN, D. LEBRUN and C. PERRIN f o r t h e i r assistance i n clearing up

some s p e c i f i c problems here discussed. And l a s t but not l e a s t I m u l d l i k e t o express t o Professor M. LEFORT my gratitude f o r encouragerrents t o undertake experiments a t the GANIL f a c i l i t y .

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